Final answer:
By using the properties of a parallelogram to equate the lengths of opposite sides, the values of x and y have been found to be 6.5 and -0.8125, respectively.
Step-by-step explanation:
To solve for the values of x and y given that LMNO is a parallelogram, we must use the properties of a parallelogram. Specifically, opposite sides of a parallelogram are equal in length. Therefore, we equate the lengths of opposite sides.
- ON = LM ⇒ 8x - 7 = 6x + 6
- OL = NM ⇒ 8y + 7 = x - 6
From the first equation, by subtracting 6x from both sides and then adding 7, we find:
- 8x - 6x = 6 + 7
- 2x = 13
- x = 13 / 2
- x = 6.5
Substituting x = 6.5 into the second equation:
- 8y + 7 = 6.5 - 6
- 8y = 0.5 - 7
- 8y = -6.5
- y = -6.5 / 8
- y = -0.8125
Thus, the values of x and y are 6.5 and -0.8125, respectively.